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Chaos and Fractals: New Frontiers of Science 2nd Edition

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Heinz-Otto Peitgen (Author)
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Heinz-Otto Peitgen (Author), Hartmut Jürgens (Author),
Dietmar Saupe (Author)
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Dietmar Saupe (Author)
4.6 out of 5 stars 16 customer reviews
ISBN-13: 978-0387202297
ISBN-10: 0387202293
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Product Details

  • Hardcover: 864 pages
  • Publisher: Springer; 2nd edition (February 3, 2004)
  • Language: English
  • ISBN-10: 0387202293
  • ISBN-13: 978-0387202297
  • Product Dimensions: 2 x 7.8 x 9.2 inches
  • Shipping Weight: 3.9 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #861,516 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

52 of 52 people found the following review helpful
Add some DEPTH to your "Recreational Mathematics"
By Daryl Anderson VINE VOICE on July 4, 2001
Format: Hardcover Verified Purchase
I spent quite a bit of time looking for a good "fractals" book. For me, this is it. It is not a book for everyone, though. I'll try to offer guidelines to help you decide if it is for you. In summary: (a) its not just a picture book, but extremely visual, (b) its not math-intense but asks for math-comfort and offers options and (c) its not only for computer jockeys, but offers repeated links to that approach.

This book is doubtless great for a high-school or college course in fractals. But I think it is also a worthy buy, albeit a pricey one, for a certain type of layperson with a fascination for mathematics presented in some depth. If you enjoy math but find some of the "popularizations" a bit too shallow, then the realm of fractals and chaos is a great place to explore in depth. This is a fine guidebook for that exploration.

"Chaos and Fractals" is not a book for the reader who is primarily fascinated with the visual representations of fractals. BUT it i!s chock-full of b/w illustrations (686 by the authors count) and nicely sprinkled with gorgeous color plates. The visual element is not central, but is very strongly represented and I found that almost every important concept was enhanced by the addition of a diagram or illustration.

This is definitely a book that delves into the mathematics of fractals. It does so in a well-crafted dual-track form. The core of the book should be comfortable and enjoyable mathematical reading for anyone with a sound and fairly current familiarity with high school math (Not that such "currency" suggests its only for youngsters! This old-timer preserves essentially that level of math by regular exposure to recreational math and the like). On the second track, the book provides mathematically in-depth views of selected topics.Read more ›
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29 of 29 people found the following review helpful
Simply a fantastic book
By Ian K. VINE VOICE on December 20, 2002
Format: Hardcover Verified Purchase
I purchased this book when it first came out, during the
initial wave of popularity of fractals and chaos theory.
Although the fadishness of chaos and fractals has died
down, a number of solid applications for this theory have
appeared in areas like computer graphics, finance,
modeling computer network traffic and data compression.
I have purchased a number of books on fractals and chaos and
how these concepts can be applied in a number of areas. I
have yet to see a better introduction to the topic. This is
a core reference and I keep coming back to it again and again.
In the spectrum of popular science books, this is definitely
on the technical end. You do not need an advanced background
in mathematics as you do for some books on chaos and fractals,
but the authors do not shy away from equations. However, the
ideas are clearly presented. I have used this book as a
reference for developing software for fractal brownian motion
and Hurst exponent estimation.
"Chaos and Fractals" covers a great deal of material. On a few
occasions I found that the algorithms or explaination were
difficult to follow. In some cases, like the generation of
Gaussian random numbers, I found better, simpler algorithms.
When this book was written, fractals and chaos were fairly new.
It is difficult to avoid comparing this book to an even thicker
book, "A New Kind of Science" by Stephen Wolfram. Although
cellular automata, the core topic of "A New Kind of Science"
are not exactly new, Wolfram claims new and profound
perspectives.Read more ›
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27 of 28 people found the following review helpful
Complex, but excellent
By angelbob@andrew.cmu.edu on September 21, 1997
Format: Hardcover
While Chaos and Fractals isn't really a book for the layman, I highly recommend it for those of you out there who want a deep and comprehensive look at these things. I've read several fractal books, some simple (FractalVision: Making Fractals Work For You), some highly mathematical (Fractal Image Compression, Science of Fractals), but this is easily the best of the lot, not only for in-depth but understandable reading, but also for separation. If you only want to learn about bifurcation in repeated iteration, or only about strange attractors, just pick the appropriate chapter. If you don't want to know about the more complex proofs, skip them; they're in small print and set off with lines to mark them as optional.

I do recommend some mathematical education and an interest in (not necessarily a talent for) proofs to get the most from this book. They cite a lot of stuff that you probably haven't seen before if you haven't had some college calculus, at least the basics. And you won't understand the more complex stuff (basic topology, mainly) unless you've had some kind of proofs-based calc course. However, even without that, it's a _really_ neat book. There's a lot here that even the layman can understand, it's just that he'll be intimidated by the set-off parts that prove the results he's only skimming.

I highly recommend this to anyone who is serious about fractals, or thinks they might try to be so in the future. It will take quite some time for even a dedicated fractal enthusiast to become bored with the book, even if it's the only one you own.
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Most Recent Customer Reviews

Great book with complex topics

Okay....
1. Have an understanding of math.
2. I am manic.
3. Supplementary and research may be necessary.

Great book with complex topics. Read more

Published 4 months ago by Derek
Look before you buy.

The 2ed is an excellent book but before buying look at the pdf at
[...] This will help you to decide if you need the printed book.

Published on October 26, 2013 by Howard Mcpherson
Great book

The content is full and easy to understand. It is perfect reference book for the beginner, as I am. I would willingly recommend it to everybody who is interested in the subject.

Published on March 21, 2013 by Ekaterina
This book is a dream come true.

This book is a dream come true.
No other publication comes close to such complete coverage of the subject.
It is highly readable even for a novice like myself. Read more

Published on September 2, 2008 by Bardo
It's all true: Best single source on fractals-but get the 1st ed.

Thanks to S.J. Will for the tip: Get the FIRST edition (used), as I did and save more than half the price, even of a used copy of this newer edition. Read more

Published on June 18, 2008 by Paul Seaman
Compare the editions

I found the 1992 edition of this book at my local public library, and was (like all the other reviewers here) very impressed at the quality. Read more

Published on April 11, 2008 by S. J. Will
Excellent tutorial on nonlinearity

At least 50% of this book can be well understood by any 1st year, exact science student. There are a couple of mathematical issues that are more senior-like, but never mind. Read more

Published on September 8, 2005 by Arturo Ortiz Tapia
A good introduction

Chaos as a physical theory began essentially in the 1970's, but as a mathematical field it has existed since the early 1900's. Read more

Published on October 4, 2003 by Dr. Lee D. Carlson
Well worth the cost

This is possibly the best and most thorough of all books on fractals. The discussion is excellent, the illustrations superb. Read more

Published on August 26, 2002 by Charles Madden
Excellent for intermediate knowledge of chaos

This book is a great entertainer for anyone who wants to spend many evenings "playing with chaos". Read more

Published on February 5, 2002 by josech

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